Abstract
We present a determination of the strong coupling constant and heavy quark masses in (2+1)-flavor QCD using lattice calculations of the moments of the pseudo-scalar quarkonium correlators at several values of the heavy valence quark mass with Highly Improved Staggered Quark (HISQ) action. We determine the strong coupling constant in the $\overline{MS}$ scheme at four low-energy scales corresponding to $m_c$, $1.5m_c$, $2m_c$, and $3m_c$, with $m_c$ being the charm quark mass. The novel feature of our analysis that up to eleven lattice spacings are used in the continuum extrapolations, with the smallest lattice spacing being $0.025$ fm. We obtain $\Lambda_{\overline{MS}}^{n_f=3}=298 \pm 16$ MeV, which is equivalent to $\alpha_s(\mu=M_Z,n_f=5)=0.1159(12)$. For the charm and bottom quark masses in the $\overline{MS}$ scheme, we obtain: $m_c(\mu=m_c,n_f=4)=1.265(10)$ GeV and $m_b(\mu=m_b,n_f=5)=4.188(37)$ GeV.
Highlights
In recent years, there has been an extensive effort toward the accurate determination of QCD parameters since the precise knowledge of these parameters is important for testing the predictions of the Standard Model
We report on the calculations of αs and the heavy quark masses in (2 þ 1)-flavor QCD using the highly improved staggered quark (HISQ) action and moments of pseudoscalar quarkonium correlators
We calculated the moments of quarkonium correlators for several heavy quark masses in (2 þ 1)-flavor QCD using the HISQ action
Summary
There has been an extensive effort toward the accurate determination of QCD parameters since the precise knowledge of these parameters is important for testing the predictions of the Standard Model. Of charm quark mass determination on the lattice is reviewed in the new FLAG report [8]. Though the current FLAG average for the charm quark mass has smaller errors than the PDG value, there are some inconsistencies in different lattice determinations The current status of the bottom quark mass calculations on the lattice is reviewed in the new FLAG report [8]. We report on the calculations of αs and the heavy quark masses in (2 þ 1)-flavor QCD using the highly improved staggered quark (HISQ) action and moments of pseudoscalar quarkonium correlators. The extracted values of the strong coupling constant and the heavy quark masses are discussed in Sec. IV and compared to other lattice and nonlattice determinations. Some technical details of the calculations are given in the Appendixes
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